LAS VEGAS -- President Barack Obama on Tuesday outlined broad proposals for putting millions of illegal immigrants on a clear path to citizenship while cracking down on businesses that employ people illegally and tightening security at the borders.

Obama hailed a bipartisan Senate group on a similar track, and said "now is the time" to fix the nation's broken system.

Potential Senate roadblocks center on how to structure the road to citizenship and on whether legislation would cover same-sex couples. Any proposal would also need to face the Republican-controlled House where opposition is sure to be stronger.

Obama, who carried Nevada in the November election with heavy Hispanic support, praised the Senate push, saying Congress is showing "a genuine desire to get this done soon."

But mindful of previous immigration efforts that have failed, he warned that the debate would be difficult and vowed to send his own legislation to Capitol Hill if lawmakers don't act quickly.

"The question now is simple," Obama said. "Do we have the resolve ... to finally put this issue behind us? I believe that we do."

Shortly after Obama finished speaking, cracks emerged between the White House and the group of eight senators, which put out their proposals the day before. Arizona Sen. Jeff Flake, one of four Republicans in the group, criticized Obama for not making a citizenship pathway contingent on tighter border security, a central tenant of the lawmakers' proposals.

House Speaker John Boehner also responded coolly. Spokesman Brendan Buck said Obama should be "careful not to drag the debate to the left and ultimately disrupt the difficult work that is ahead in the House and Senate."